Inflationary de Sitter solutions from superstrings

In the framework of superstring compactifications with N=1 supersymmetry spontaneously broken (by either geometrical fluxes, branes or else), we show the existence of new inflationary solutions. The time-trajectory of the scale factor of the metric a, the supersymmetry breaking scale m≡m(Φ) and the temperature T are such that am and aT remain constant. These solutions request the presence of special moduli-fields: (i) The universal “no-scale-modulus” Φ, which appears in all N=1 effective supergravity theories and defines the supersymmetry breaking scale m(Φ). (ii) The modulus Φs, which appears in a very large class of string compactifications and has a Φ-dependent kinetic term. During the time evolution, a4ρs remains constant as well (ρs being the energy density induced by the motion of Φs). The cosmological term Λ(am), the curvature term k(am,aT) and the radiation term cR=a4ρ are dynamically generated in a controllable way by radiative and temperature corrections; they are effectively constant during the time evolution. Depending on Λ, k and cR, either a first or second order phase transition can occur in the cosmological scenario. In the first case, an instantonic Euclidean solution exists and connects via tunneling the inflationary evolution to another cosmological branch. The latter starts with a big bang and, in the case the transition does not occur, ends with a big crunch. In the second case, the big bang and the inflationary phase are smoothly connected.